A multidimensional Szemerédi theorem in integers

Jingwei Guo, Changxing Miao, Guoqing Zhan

For any integer $n\ge 2$, let $(m_1,\dots ,m_n)$ be a strictly increasing $n$-tuple of positive integers. We show that any subset $A\subset [N{]}^n$ of density at least $(\log…